With about 22%, the transport sector is one of the largest global emitters of the greenhouse gas CO₂. Long-distance road freight transport accounts for a large and rising share within this sector. For this reason, in February 2019, the European Union agreed to introduce CO₂ emission standards following Canada, China, Japan and the United States. One way to reduce CO₂ emissions from long-distance road freight transport is to use alternative powertrains in trucks — especially heavy-duty vehicles (HDV) because of their high mileage, weight and fuel consumption. Multiple alternative fuels and powertrains (AFPs) have been proposed as potential options to lower CO₂ emissions. However, the current research does not paint a clear picture of the path towards decarbonizing transport that uses AFPs in HDVs. The aim of this literature review is to understand the current state of research on the market diffusion of HDVs with alternative powertrains. We present a summary of market diffusion studies of AFPs in HDVs, including their methods, main findings and policy recommendations. We compare and synthesize the results of these studies to identify strengths and weaknesses in the field, and to propose further options to improve AFP HDV market diffusion modelling. ... mehrAll the studies expect AFPs on a small scale in their reference scenarios under current regulations. In climate protection scenarios, however, AFPs dominate the market, indicating their positive effect on CO₂ reduction. There is a high degree of uncertainty regarding the emergence of a superior AFP technology for HDVs. The authors of this review recommend more research into policy measures, and that infrastructure development and energy supply should be included in order to obtain a holistic understanding of modelling AFP market diffusion for HDVs.